Osaka Journal of Mathematics

On the splitting principle of bundle gerbe modules

Atsushi Tomoda

Full-text: Open access


We introduce the notion of an $n$-trivialization and a compatible curving and construct the splitting of bundle gerbe modules to define the twisted Chern classes and the twisted Chern character for bundle gerbe modules in terms of algebraic topology. Moreover, we prove that the latter coincides with the twisted Chern character due to Bouwknegt-Carey-Mathai-Murray-Stevenson [1] if the bundle gerbe is given an $n$-trivialization and a compatible curving.

Article information

Osaka J. Math., Volume 44, Number 1 (2007), 231-246.

First available in Project Euclid: 19 March 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55R65: Generalizations of fiber spaces and bundles
Secondary: 55R20: Spectral sequences and homology of fiber spaces [See also 55Txx]


Tomoda, Atsushi. On the splitting principle of bundle gerbe modules. Osaka J. Math. 44 (2007), no. 1, 231--246.

Export citation


  • P. Bouwknegt, A. Carey, V. Mathai, M.K. Murray, and D. Stevenson: Twisted $K$-theory and $K$-theory of bundle gerbes, Comm. Math. Phys. 228 (2002), 17--45.
  • M.K. Murray: Bundle gerbes, J. London. Math. Soc. (2) 54 (1996), 403--416.
  • M.K. Murray and D. Stevenson: Bundle gerbes: stable isomorphism and local theory, J. London. Math. Soc. (2) 62 (2000), 925--937.
  • D. Husemoller: Fibre Bundles, second edition, Graduate Texts in Math. 20, Springer-Verlag, New York, 1975.